IPS is best for performance. OLED is best for visual fidelity. Curved screens and any refresh rate over 144Hz are gimmicks.
Depends on what you mean by performance. Response times, input lags, color, viewing angles.
There is a measurable, both qualitatively and quantitively, difference with extreme refresh rates. But it only applies to fast paced first person shooters and games where you are regularly seeing FPS in the hundreds. A lot depends on the visual sensitivity of the person and their response times.
TN fast response times, poor color, usually the worst vertical viewing angles and fairly bad horizontal viewing angles.
VA also has generally fast response times, okay color. These are usually your curved screens because the color accuracy depends on being straight on to the pixels. (A lot of cheaper large TVs are VA, because at a distance it doesn't matter as much)
IPS/PLS/AVHA are your good color reproduction and viewing angles, and of late they have gotten response times down quite a bit and AVHA and similar technologies are responsible for the fast refresh "IPS" panels. High end accurate monitors are still IPS and they can have response times in the teens.
OLED is uncommon and expensive. Ideal black levels no local dimming issues, but may have longevity issues (dim over time) and burn in. Which isn't ideal for games with static displays.
MINI LED backlight is a way to avoid issues with local dimming.
QLED/WRGB OLED are the more recent interesting ones. Kind of a hybrid LCD/OLED technology.
Also, don't take response time figures from the vendors as accurate. Seek out independent reviews.